Question

A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

Answer 1

Answer:

the shadow is moving with 12ft/s from the woman

Explanation:

let the distance from the pole to the shadow tip be L

$\frac{10}{6} = \frac{L}{x}$

$L=\frac{5}{3}x$

$\frac{\mathrm{d} (QR)}{\mathrm{d} t}= 8ft/s$

$\frac{\mathrm{d} (L-x)}{\mathrm{d} t}= 8ft/s$

$\frac{\mathrm{d} (L)}{\mathrm{d} t}-\frac{\mathrm{d} (x)}{\mathrm{d} t}= 8ft/s$

$\frac{\mathrm{d} (L)}{\mathrm{d} t}=\frac{5}{3}\frac{\mathrm{d} (x)}{\mathrm{d} t}$

$\frac{\mathrm{d} (x)}{\mathrm{d} t}=12ft/s$

$\frac{\mathrm{d} (L)}{\mathrm{d} t}=16ft/s$

hence the shadow is moving with 12ft/s from the woman